NEW YORK — Mayor Michael Bloomberg sought to strike a humble tone Friday as he began his third term by promising "to listen and to lead" and to take a fresh look at the challenges facing the city.

The 67-year-old billionaire acknowledged the unusual circumstances that landed him on the steps of City Hall to take the oath of office for another four years. A city term-limit law had barred officeholders from seeking a third, consecutive term, but he orchestrated a last-minute law change that let him run again in 2009.

"This term is a special opportunity, one that comes with extraordinary responsibilities," Bloomberg said. "I realize, too, that the building behind me is yours, and the job in front of me is to listen and to lead."

The former CEO first took office as a Republican in 2002 and was re-elected by a landslide in 2005. Now an independent, his most recent re-election was more difficult as he faced voter resentment for the way he went about changing term-limits law. His margin of victory over his Democratic challenger was far narrower than predicted — he won by slightly less than five percentage points.

Bloomberg heads into a third term with a little less political capital and a changed City Hall landscape. Twelve of the City Council's 51 members are new and two citywide officials who took office Friday, Comptroller John Liu and Public Advocate Bill de Blasio, have warned they are not afraid to stand up to the mayor.

About 2,000 invited guests, given mugs of hot cider to stay warm during the outdoor program, watched Bloomberg, Liu and de Blasio take the oath of office.

Bloomberg said he would take on the national issue of immigration reform similar to the way he focused on gun control in his second term. The mayor established the group Mayors Against Illegal Guns, which has pushed its agenda on Capitol Hill and in local political races throughout the nation.

Bloomberg did not give specifics on what he was planning to do, but said he would seek a bipartisan coalition to "support President Obama's call for comprehensive immigration reform."

In the past, Bloomberg has called for giving all undocumented immigrants the opportunity for citizenship. He also has advocated the idea of a DNA or fingerprint database to track and verify legal immigrant workers.

He said the city's future depends on honoring "the ideals that have lit the lamp of liberty in our harbor for more than a century."

Liu, the new comptroller, noted in his speech that "economic misery cuts ever deeper into families across the city."

The first Asian-American in citywide office also thanked his parents, who he said "could have had a lot in Taiwan but they gave everything up so their kids could grow up American."

The mayor, whose fortune is estimated at $17.5 billion by Forbes magazine, spent more than $102 million on his re-election campaign. But he clamped down on lavish spending for the inauguration, foregoing a traditional party and instead spending the day visiting people doing volunteer work throughout the city.

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